Determine the maximum bending moment, Mechanical Engineering

Assignment Help:

Determine the maximum bending moment:

A 12 m span simply supported beam is carrying a consistently distributed load of 2 kN/m over a length of 6 m from the left end and point loads 6 kN, 3 kN and 4 kN at distances of 7 m, 8 m and 9 m, respectively. Draw BM diagram and SF diagram for the beam and determine the maximum bending moment.

2454_Determine the maximum bending moment.png

Figure

Solution

Taking moments around A, and equating to zero.

RB × 12 - (4 × 9) - (3 × 8) - (6 × 7) - 2 × 6 ×(6/2)   = 0

Therefore,        RB = 11.5 kN, and

RA = (2 × 6) + 6 + 3 + 4 - RB = 25 - 11.5 = 13.5 kN

Shear Force (beginning from the left end)

 SF at A, FA = + 13.5 kN

SF at C, FC = + 13.5 - 2 × 6 = + 1.5 kN

SF just left of   D = + 1.5 kN

 SF just right of D = + 1.5 - 6 = - 4.5 kN

SF just left of  E = - 4.5 kN

SF just right of E = - 4.5 - 3 = - 7.5 kN

 SF just left of   F = - 7.5 kN

SF just right of F = - 7.5 - 4 = - 11.5 kN

SF just left of   B = - 11.5 kN = Reaction at B.

Bending Moment

BM at A, MA = 0

BM at C, M  = (13.5 × 6) - 2 × (6 ×(6/2))   = 45 kNm (considering left side)

BM at D, MD = (11.5× 5) - (4 × 2) - (3 × 1) = 46.5 kN m (considering right side)

BM at E,

ME = (11.5 × 4) - (4 × 1) = 42 kN m

BM at F,

MF = (11.5 × 3) = 34.5 kN m

The maximum bending moment take place at D where the shear force changes sign.

                       Mmax = 46.5 kN m.


Related Discussions:- Determine the maximum bending moment

Find span of the beam, A beam is simply supported and carries a uniformly d...

A beam is simply supported and carries a uniformly distributed load of 40kn/m run over whole length or span. The section of the beam is rectangular having depth as 500mm. If the s

Example of free body diagram - mechanics, Example of free body diagram: ...

Example of free body diagram: The thr e e spheres A , B , C are placed in groove shown in the figure given below. The diameter of each sphere is 100mm. Sketch the free

Illustrate the term directional solidification, Describe some special kind ...

Describe some special kind of patterns and indicate the production circumstances in which each would be need. Illustrate the term Directional solidification as applied in castin

Mechanism of laser welding, MECHANISM OF LASER WELDING   Laser weldi...

MECHANISM OF LASER WELDING   Laser welding of metals is performed with beams focused to irradiate levels in the range of 106 to 107 W / cm 2 . At such power densities, melti

Optimization, consider the following LPP max z=9x1+8x2+5x3 subject to 2x1+3...

consider the following LPP max z=9x1+8x2+5x3 subject to 2x1+3x2+x3 5x1+4x2+3x3 x1,x2,x3>_0 (a)solve using simlex method (b)hence using the sesitivity analysis,find the new optima

Design analysis drafting machine, hello,my name is mustapha from iran I wa...

hello,my name is mustapha from iran I want design piston engine (structure design cranckshaft ,rod,bearing,...)

Fms, fms computer control system

fms computer control system

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd